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Questions related to computability theory, a.k.a. recursion theory

1 vote
1 answer
97 views

Is the following function computable? is it total?

I have the following function: $f : N \to N $ and $f(n)= \max_{i \leq w(n)} g_{i}(n)$ with $g_1, g_2,...g_{w(n)}$ being an enumeration of all computable functions $g_i$, and $w : N \to N$ being any no …
Joey's user avatar
  • 53
-1 votes
1 answer
155 views

Turing machine to find maximum of an infinite set

Given a set that is infinite but still countable, does a TM exist that goes over every element in the set and finds the maximum? Is this a computable function?
Joey's user avatar
  • 53